There is "thru-hiking," which are those really long deals where someone will hike the whole Arizona trail, 800 miles in one pop, or the Appalachian Trail, over 2500 miles, etc. (Takes a LOT of planning and time.) You will see references to the AZT, PCT, AT, and CDT, and GET as thru-hiker's trails. And there is a kind of thru-hiking which is called fast-packing where they try to do a long trail faster than anyone else has ever done it before (and one wonders if they see anything at all...) And yet another kind of thru-hiking is called "section hiking" where the person bites off a big chunk of a long trail but not the whole thing at one time, and keeps going back a week or so at a time, until finished. (Some people take 20 years to section-hike the Appalachian Trail, others only 4 months or so to thru-hike it!)
Then there is "bushwhacking" which is off-trail, and "scrambling" which is where you might have to use your hands sometimes, and is also off-trail. And you get into the catclaw and wish you had gloves, and then you notice you are the only one in the group wearing shorts and no gloves, and you understand your terrible mistake...
Then there is "peak bagging" which is this kind of fun but rather ridiculously obsessive hobby of hiking to the tops of peaks and keeping a list of which ones you did--people try to get 500 or 1000 of them, etc. It often doesn't matter if they are really small, they just have to be on some list or another. The Arizona Big List, or the SAHC 400 list, or the Angeles Chapter Desert Peaks List, or the Colorado 14ers list, etc. Sort of like birding, but with slightly different silly clothes.
And "canyoneering" which often requires ropes and rock climbing skills and wetsuits and flotation devices, etc. Very specialized. (You can take classes in that.) Bushwhacking, scrambling, canyoneering and peakbagging can be done as dayhikes OR as backpacks.
Confused yet? I am!

There are a bunch more terms, but those are enough for now. Just as long as you don't start calling it "trekking" I'll be happy... Trekking is what you do in Nepal. The porters carry everything, all you need is a whole lot of money. We live in the western United States, and we are hikers.